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Robust Linear Mixed Models with Heterogeneity in theRandom-Effects PopulationCelso Rômulo Barbosa CabralDepartamento de Estatística, Universidade Federal do Amazonas, BrazilVíctor Hugo LachosDepartamento de Estatística, Universidade Estatual de Campinas, BrazilMaria Regina MadrugaFaculdade de Estatística, Universidade Federal do Pará, BrazilWe present a new class of models to fit longitudinal data, obtained with a suitable modification ofthe classical linear mixed-effects model, by supposing that, for each sample unit, the joint distributionof the random effect and the random error is a finite mixture of scale mixtures of multivariate skewnormaldistributions, allowing us to model the data in a more flexible way, taking into account skewness,multimodality and discrepant observations at the same time. The scale mixtures of skew-normal form anattractive class of asymmetric heavy-tailed distributions that includes the skew-normal, skew-Student-t,skew-slash and the skew-contaminated normal distributions as special cases, being a flexible alternativeto the use of the corresponding symmetric distributions in this type of models. A simple MCMC Gibbstypealgorithm for posterior Bayesian inference is employed. In order to illustrate the usefulness of theproposed methodology, one artificial and one real data set – from the Framingham cholesterol study –are analyzed.Keywords: Bayesian estimation; Framingham cholesterol study; finite mixtures; linear mixed model;MCMC; skew-normal distribution.Acknowledgements: The authors acknowledge the partial financial support from FAPESP, CNPqand CAPES.63